Question

Write in point-slope form an equation of the line that passes through the point (3,−5) with slope −4.

Answer 1

Answer:

Write in point-slope form an equation of the line that passes through the point (3,−5) with slope −4.

Write in point-slope form an equation of the line that passes through the point (3,−5) with slope −4.

Answer 2

Given Question :-

• Write in point-slope form an equation of the line that passes through the point (3,−5) with slope −4.

ANSWER

GIVEN :-

• A line passes through the point (3, - 5) having slope - 4.

TO FIND :-

• The equation of line

CONCEPT USED :-

Slope Point Form of a Line

• Let us consider a line which passes through the point (a, b) having slope 'm', then equation of line is given by y - b = m(x - a).

Let do it now!!.

CALCULATION :-

Given

• A line passes through the point (3, - 5) and having slope - 4.

So,

We know,

• Equation of line using slope point form is given by

$\rm :\longmapsto\:y - b = m(x - a)$

Here,

• a = 3

• b = - 5

• m = - 4

On substituting the values of a, b and m, we get

$\rm :\longmapsto\:y + 5 = - 4(x - 3)$

$\rm :\longmapsto\:y + 5 = - 4x + 12$

$\rm :\implies\:4x + y - 7 = 0 \: is \: required \: equation \: of \: line.$

Additional Information

Additional Information Different forms of equations of a straight line

1. Equations of horizontal and vertical lines

• Equation of the lines which are horizontal or parallel to the X-axis is y = a, where a is the y – coordinate of the points on the line.
• Similarly, equation of a straight line which is vertical or parallel to Y-axis is x = a, where a is the x-coordinate of the points on the line

2. Point-slope form equation of line

• Consider a non-vertical line L whose slope is m, A(x,y) be an arbitrary point on the line and P(a, b) be the fixed point on the same line. Equation of line is given by
• y - b = m(x - a)

3. Slope-intercept form equation of line

• Consider a line whose slope is m which cuts the Y-axis at a distance ‘a’ from the origin. Then the distance a is called the y– intercept of the line. The point at which the line cuts y-axis will be (0,a). Then equation of line is given by
• y = mx + a.

4. Intercept Form of Line

• Consider a line L having x– intercept a and y– intercept b, then the line passes through  X– axis at (a,0) and Y– axis at (0,b).
• Equation of line is given by x/a + y/b = 1.

5. Normal form of Line

• Consider a perpendicular from the origin having length p to line L and it makes an angle β with the positive X-axis.
• Then, equation of line is given by x cosβ + y sinβ = p.